An apparatus of the kind referred to above is disclosed in German patent No. 16 22 484. In this apparatus, a small region of a moving band is illuminated by a pulsed light source and an image of a diaphragm illuminated by the light source is formed on the band. German patent No. 16 22 484 refers to this irradiated area as being a field limiting image. An image of a middle zone of this irradiated area is formed on a receiver, so that the measuring area from which the reflected radiation is detected by the measuring device is smaller than the irradiated area. This known apparatus has the disadvantage that the measurement result is dependent on the distance between the band and the measuring device. In many machines in which the reflectance or the color of moving bands must be measured, however, this distance is not constant, because at the locations where it is possible to accommodate a measuring device, the band flutters.